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Szemer\'edi-Trotter bounds for tubes and applications

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arxiv 2406.06884 v3 pith:YQYICKOQ submitted 2024-06-11 math.CA

Ciprian Demeter , Hong Wang This is my paper · ORCID
classification math.CA
keywords estimatesplanartubesapplicationsapplyboundsconditionscurves
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We prove sharp estimates for incidences involving planar tubes that satisfy packing conditions. We apply them to improve the estimates for the Fourier transform of fractal measures supported on planar curves.

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  1. Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities

    math.CA 2024-11 conditional novelty 8.0 of 10

    The authors prove the restriction conjecture for p > 22/7 in R^3 and new higher-dimensional bounds by combining decoupling theorems with new two-ends Furstenberg incidence estimates.

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